In Exercises 16-18, determine whether the given (2 x 3) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line; that is, give equa- tions of the form x = at +b, y = ct+d₂z = et + f. 16. 2x₁ + x₂ + x3 = 3 17. x₁ + 2x₂-x3 = 2 -2x₁ + x₂-x3 = 1 x₁ + x₂ + x3 = 3 18.) x+3x2-2x3 = -1 2x₁ + 6x2 - 4x3 = -2

In Exercises 16-18, determine whether the given (2 x 3) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line; that is, give equa- tions of the form x = at +b, y = ct+d₂z = et + f. 16. 2x₁ + x₂ + x3 = 3 17. x₁ + 2x₂-x3 = 2 -2x₁ + x₂-x3 = 1 x₁ + x₂ + x3 = 3 18.) x+3x2-2x3 = -1 2x₁ + 6x2 - 4x3 = -2

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 20E

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